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The radiation pattern is usually a factory set characteristic of telecommunication equipment. By using an antenna array, the radiation pattern can be shaped in order to optimise the covered region. Antenna pattern synthesis consists of determining the phase and the amplitude to apply to each radiating element of the network for obtaining the targeted radiation pattern. A radiation pattern synthesis technique based on the variational method is presented. The goal is expressed in terms of antenna radiation pattern and special attention is given to the computation time. We calculate an optimised mask function from specifications obtained during a surroundings learning step. The resulting radiation pattern is optimised in terms of power waste. Simulated and measured radiation patterns are presented in order to illustrate the performances of the method. The speed of convergence makes this method well suited to systems where radiation patterns must be modified in real time.